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Evolution Equations of Hyperbolic and Schrödinger Type

Asymptotics, Estimates and Nonlinearities

  • Book
  • © 2012

Overview

Editors:
  1. Michael Ruzhansky

    1. , Department of Mathematics, Imperial College London, London, United Kingdom

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  2. Mitsuru Sugimoto

    1. , Graduate School of Mathematics, Nagoya University, Nagoya, Japan

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    You can also search for this editor in PubMed   Google Scholar

  3. Jens Wirth

    1. , Fachbereich Mathematik, Universität Stuttgart, Stuttgart, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • Overview of a variety of ongoing current research in the field of equations of hyperbolic and Schrödinger types Can serve as a quick introduction to different aspects of the theory of evolution partial differential equations from pure and applied points of view ?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Mathematics (PM, volume 301)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
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  2. Divergence-type Operators: Spectral Theory and Spacetime Estimates

    • Matania Ben-Artzi
    Pages 1-40

  3. Kinetic Models of Chemotaxis

    • Nikolaos Bournaveas, Vincent Calvez
    Pages 41-52

  4. Modulus of Continuity and Decay at Infinity in Evolution Equations with Real Characteristics

    • Massimo Cicognani, Ferruccio Colombini
    Pages 53-62

  5. Time-Frequency Analysis of Schrödinger Propagators

    • Elena Cordero, Fabio Nicola, Luigi Rodino
    Pages 63-85

  6. Geometric Regularization on Riemannian and Lorentzian Manifolds

    • Shantanu Dave, Günther Hörmann, Michael Kunzinger
    Pages 87-102

  7. A Remark on the Uniqueness for Backward Parabolic Operators with non-Lipschitz-continuous Coefficients

    • Daniele Del Santo
    Pages 103-114

  8. Dispersive Properties of Schrödinger Operators in the Absence of a Resonance at Zero Energy in 3D

    • Vladimir Georgiev, Mirko Tarulli
    Pages 115-143

  9. Decay Estimates for the Supercritical 3-D Schrödinger Equation with Rapidly Decreasing Potential

    • Vladimir Georgiev, Bozhidar Velichkov
    Pages 145-162

  10. Wave Equations on Non-smooth Space-times

    • Günther Hörmann, Michael Kunzinger, Roland Steinbauer
    Pages 163-186

  11. Lower Bounds for the Lifespan of Solutions to Nonlinear Wave Equations in Elasticity

    • Hideo Kubo
    Pages 187-212

  12. Representation Formula of the Resolvent for Wave Equation with a Potential Outside the Convex Obstacle

    • Tokio Matsuyama
    Pages 213-225

  13. On the Scattering on a Loop-shaped Graph

    • K. Mochizuki, I. Yu. Trooshin
    Pages 227-245

  14. On the Cauchy Problem for Hyperbolic Operators with Double Characteristics

    • Cesare Parenti, Alberto Parmeggiani
    Pages 247-266

  15. Modulation Spaces and Nonlinear Evolution Equations

    • Michael Ruzhansky, Mitsuru Sugimoto, Baoxiang Wang
    Pages 267-283

  16. An Optimal Control Problem for a Nonlinear Hyperbolic Equation with an Infinite Time Horizon

    • Simon Serovajsky, Kanat Shakenov
    Pages 285-300

  17. Local in Space Energy Estimates for Second-order Hyperbolic Equations

    • Sergio Spagnolo, Giovanni Taglialatela
    Pages 301-313

  18. The Final Problem on the Optimality of the General Theory for Nonlinear Wave Equations

    • Hiroyuki Takamura, Kyouhei Wakasa
    Pages 315-324
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Keywords

About this book

Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions  and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area. ​

Editors and Affiliations

  • , Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

  • , Graduate School of Mathematics, Nagoya University, Nagoya, Japan

    Mitsuru Sugimoto

  • , Fachbereich Mathematik, Universität Stuttgart, Stuttgart, Germany

    Jens Wirth

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